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For bond that's formed between two identical atoms, I naively understand that one molecular orbital is a bonding orbital and the other is an antibonding one, and I believe they have to do with the superposition of the atoms' wavefunctions to constructively or destructively interfere.

For metal lattices (without any impurities), there's a lot more than a combination of two atoms' wavefunctions. I've heard of the conduction and valence band, which I believe are molecular orbitals of constructively and deconstructively interfering wavefunctions. I'm wondering, if you look for "thinner" bands between these two, would they look like wave interference pattern? (like a two-slit experiment) If they do, could I treat the the valence band as a "principal maximima" and the conduction band as a "principal maxima"?

Is this even a coherent question, or is my current understanding of molecular orbitals in solids very very wrong?

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  • $\begingroup$ Related: chemistry.stackexchange.com/questions/85740/… $\endgroup$ May 26, 2023 at 8:51
  • $\begingroup$ I know that there's almost a 'continuum' of orbitals in a metal right by each other, and I thought that two particular 'dense' points were called the valence and conduction band for being dense in bonding and antibonding orbitals, respectively. I was wondering if there were bands that weren't as dense as these two, but more dense than the 'background' that was similar to what I might see in slit diffraction. $\endgroup$
    – Samuel Han
    May 26, 2023 at 15:20
  • $\begingroup$ Got it. No, bands are not points, and there may not be particularly dense points at all, and when there are, they don't mean all that much. $\endgroup$ May 26, 2023 at 17:23

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The simplest model is that of a 'free electron gas', in Chemistry this is called the 'particle in a box', and produces a set of energy levels that are filled with electrons to the Fermi level. However, a metal has regularly arranged atoms and these produce a periodic potential which perturb the electrons' energy levels producing energy gaps in which energy levels are forbidden. This is sometimes called the 'nearly free electron model'. In this model we use the idea of Bragg reflection of electron waves in the crystal, which is related to but different from your idea of multiple slit interference. If you want more detailed information look at Kittel, 'Introduction to Solid State Physics', although published a while ago now the explanations are very clear.

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